Proper Orthogonal Decomposition Methods for Partial Differential Equations (Mathematics in Science and Engineering) 1st Edition by Zhendong Luo (PDF)

Description

Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load and alleviating the accumulation of truncation error in the computational process. Introduces the foundations of finite-differences, finite-elements and finite-volume-elements. Models of time-dependent PDEs are presented, with detailed numerical procedures, implementation and error analysis. Output numerical data are plotted in graphics and compared using standard traditional methods. These models contain parabolic, hyperbolic and nonlinear systems of PDEs, suitable for the user to learn and adapt methods to their own R&D problems.

User’s Reviews

Editorial Reviews: Review “This book details the application of the Proper Orthogonal Decomposition (POD) to instationary problems whose spatial semidiscretization is done either by Finite Difference (FD), Finite Element (FE) or Finite Volume (FV) methods. These three discretization methods correspond to the 3 main chapters of the book.” –zbMATH Review This guide evaluates the potential applications of the Proper Orthogonal Decomposition (POD) reduced-order numerical methods for time-dependent partial differential equations From the Back Cover Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load, and alleviating the accumulation of truncation error in the computational process. The work is self-contained. At the beginning of each chapter, the foundations of finite-differences, finite-elements and finite-volume-elements are introduced. Models are time-dependent PDEs are presented, with detailed numerical procedures, implementation and error analysis. Output numerical data are plotted in graphics and compared with those by the standard traditional methods. These models contain parabolic, hyperbolic and nonlinear systems of PDEs suitable for the user to learn and adapt methods to their own problems across research and development. About the Author Zhendong Luo is Professor of Mathematics at North China Electric Power University, Beijing, China. Luo is heavily involved in the areas of Optimizing Numerical Methods of PDEs; Finite Element Methods; Finite Difference Scheme; Finite Volume Element Methods; Spectral-Finite Methods; and Computational Fluid Dynamics. For the last 12 years, Luo has worked mainly on Reduced Order Numerical Methods based on Proper Orthogonal Decomposition Technique for Time Dependent Partial Differential Equations. Read more

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